Pattern on Easter Egg for 3D-Printing
What I did was use a bezier circle to curve the shape I used to cut into my sphere. A simple curve deform with Ctrl+P after selecting my imported .svg, then the circle. 

As for the pattern cut into the sphere:

I first removed doubles on the imported curve after converting it to a mesh object with W>remove doubles and then used limited dissolve to clean it up a little more and recalculated normals with  Ctrl+N. Finally extruding the object to give it the thickness I wanted. 

The last step for the cut itself, was joining the sphere and pattern objects as one, then going to edit mode, and selecting only the imported object and placing it where needed. Then finally, via the Spacebar menu, searched for Boolean, and the hole was cut. 

Here's a little .gif showing that part of the process. 

Edit in response to comment:

This will only address the first of the images and should get you in the direction of the desired result.


Add a UV sphere, in the operator panel, increase rings and segments as desired. I used 120 segments, and 60 rings. Scale along the Z axis to the appropriate shape.
Apply a decimate modifier set to unsubdivide with one iteration.

In edit mode select all face loops that will be kept.





Invert selection with Ctrl+I and then press X and delete the selected faces.





Select the face loops that should be raised with Shift+Alt+RMB and then press Alt+E>Region(vertex normals)





Tab back into object mode, add a solidify modifier, adjust to the desired thickness. Add subsurf if desired.




Using these steps you can go in a few directions and should be able to get the results you're after.